The Linear Stability of Reissner-Nordstrom Spacetime: The Full Subextremal Range |Q| < M

We prove the linear stability of subextremal Reissner-Nordstrom spacetimes as solutions to the Einstein-Maxwell equation. We make use of a novel representation of gauge-invariant quantities which satisfy a symmetric system of coupled wave equations. This system is composed of two of the three equations derived in our previous works (Giorgi in Ann Henri Poincar, 21: 24852580, 2020; Giorgi in Class Quantum Grav 36:205001, 2019), where the estimates required arbitrary smallness of the charge. Here, the estimates are obtained by defining a combined energy-momentum tensor for the system in terms of the symmetric structure of the right hand sides of the equations. We obtain boundedness of the energy, Morawetz estimates and decay for the full subextremal range vertical bar Q vertical bar < M, completely in physical space. Such decay estimates, together with the estimates for the gauge-dependent quantities of the perturbations obtained in Giorgi (Ann PDE 6:8, 2020), settle the problem of linear stability to gravitational and electromagnetic perturbations of Reissner-Nordstrom solution in the full subextremal range vertical bar Q vertical bar < M.